Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x-5y &= -1 \\ -7x-5y &= 5\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-5y = 7x+5$ Divide both sides by $-5$ to isolate $y$ $y = {-\dfrac{7}{5}x - 1}$ Substitute this expression for $y$ in the first equation. $-4x-5({-\dfrac{7}{5}x - 1}) = -1$ $-4x + 7x + 5 = -1$ Simplify by combining terms, then solve for $x$ $3x + 5 = -1$ $3x = -6$ $x = -2$ Substitute $-2$ for $x$ back into the top equation. $-4( -2)-5y = -1$ $8-5y = -1$ $-5y = -9$ $y = \dfrac{9}{5}$ The solution is $\enspace x = -2, \enspace y = \dfrac{9}{5}$.